Physics-informed neural networks for solving partial differential equations
In recent years, Physics-Informed Neural Networks (PINNs) have gained popularity, across different engineering disciplines, as an alternative to conventional numerical techniques for solving partial differential equations (PDEs). PINNs are physics-based deep learning frameworks that seamlessly integrate the measurements and the PDE in a multitask loss function. In forward problems, these measurements are initial (IC) and boundary conditions (BCs), whereas in the inverse problems they are sparse measurements such as temperature recorded by thermocouples. The scope of PDEs applicable in PINNs could include integer-order PDEs, integro-differential equations, fractional PDEs or even stochastic PDEs. This chapter presents a brief state-of-the-art overview of PINNs for solving PDEs. Our discussion primarily focuses on solution to parametric problems, approaches to tackle stiff-PDEs and problems involving complex geometries. The advantages and disadvantages of several PINNs frameworks are also discussed.